MathDB

If $\phi(n)|n-1$, then prove this problem :-)

Source: Korea NMO 1998

August 20, 2011

number theoryrelatively primenumber theory unsolved

Problem Statement

Denote by

\phi(n)

for all

n\in\mathbb{N}

the number of positive integer smaller than

n

and relatively prime to

n

. Also, denote by

\omega(n)

for all

n\in\mathbb{N}

the number of prime divisors of

n

. Given that

\phi(n)|n-1

and

\omega(n)\leq 3

. Prove that

n

is a prime number.